Question

The equation: ax^2+bx+c=0 may have two real solutions, one real solution, or a conjugate complex pair of solutions. Assuming there are two real solutions, and a > 0, the smaller is x= ________. (This is the celebrated quadratic formula) Find the smaller solution.

Answer 1

Given:

The quadratic equation,

`ax^2+bx+c=0`

As the given equation has two real solution and a>0.

The solution is given by the formula,

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{For a<0 the value for }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\text{ will be positive and it will give the greater value.} \\ \text{ For a>0 it will give the value obtained will always be smaller.} \end{gathered}`